The model also reasonably predicts the overshoot response observed after the two-step memory experiment.
Here we present an adaptive time step memory method for smooth functions applied to the Grünwald Letnikov fractional diffusion derivative.
Our analysis is divided into two cases: (i) no memory players, where players do not remember previous decisions, and (ii) one-step memory players, where the offers depend on players' last decision.
Without loss of generality, these probabilities are derived in the following sections for the max-rate and proportional fair algorithms, which, in both cases, can be modeled by a service-vacation process with one-step memory (D = 1).
A D-step memory in the service-vacation process represents the scheduling dependence on D previous decisions and can be used to account for an increased degree of fairness between users.
Case (b) combined with one-step memory players (ii), we verified, via MC simulations that, for the same number of iterations, the responder obtains different cumulative payoffs by setting different cutoff values.
In one-step memory service-vacation processes, scheduling decisions only rely on the actual system state, and thus, the state transition probabilities in (2) can be simplified to P i, j u = Pr z ν + 1 u, y ν + 1 u | z ν u, y ν u.
For this simulation, the previous time-step was also added to the current state (i.e., sAi−1+siA), simulating a one-step memory.
Furthermore, during these steps, the memory space to accommodate reads is dynamically allocated and deallocated, which might induce further mutual exclusion operations within the memory allocator.
We can notice that, for a given version, loop-fusion divides the complexity by a factor 1.2 (by rewriting image integral steps) and memory accesses by a factor 2.5 by avoiding LOADs and STOREs of temporary results.
